Let $U(n)$ denote the unitary group. That is,
$$ U(n) = \{A \in GL_n(\mathbb C)\mid A^\ast A = I\}$$
Wikipedia states:
"The unitary group $U(n)$ is a real Lie group of dimension $n^2$. "
There seem to be two typos: one, unitary matrices are complex. So it should be a statement about complex Lie group. The other typo is $n^2$: $n^2$ is the dimension of $GL_n$ and $U(n)$ is a proper subgroup so clearly its dimension must be smaller than $n^2$.
What's the dimension of $U(n)$?
The unitary group $U(n)$ is a real Lie group of $GL(n, \mathbb{C})$. We can forget about the complex structure on $GL(n, \mathbb{C})$ and hence view it as a real Lie subgroup of (real) dimension $2 n^2$, which is greater than $\dim U(n) = n^2$.
Note, by the way, that $GL_+(n, \mathbb{R}) := \{A \in GL(n, \mathbb{R}) : \det A > 0\}$ is a proper subgroup of $GL(n, \mathbb{R})$ but $\dim GL_+(n, \mathbb{R}) = n^2 = \dim GL(n, \mathbb{R})$.